bg slope 08nov v2 - fish
TRANSCRIPT
Updated stock assessment of blue
grenadier Macruronus novaezelandiae
based on data up to 2007
G.N. Tuck1
1. CSIRO Marine and Atmospheric Research, Castray Esplanade, Hobart 7000.
Slope Resource Assessment Group 17/18 November 2008 Hobart, Tasmania
Enquiries should be addressed to:
Geoff Tuck
CSIRO Marine and Atmospheric Research
1 Castray Esplanade, Hobart, Tas, 7000
03 62325222
Important Notice
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CONTENTS
1. SUMMARY ................................................................................................ 1
2. INTRODUCTION ....................................................................................... 1
3. THE FISHERY........................................................................................... 2
4. DATA......................................................................................................... 2
4.1 Catch ................................................................................................ 2
4.2 Catch rates....................................................................................... 3
4.3 Length Frequencies and Catch-at-age .......................................... 5
4.4 Age-reading error ............................................................................ 8
4.5 Acoustic survey estimates ............................................................. 9
4.6 Egg survey estimates ..................................................................... 9
4.7 Parameters of breeding biology .................................................. 11
5. ANALYTIC APPROACH.......................................................................... 11
5.1 The population dynamics model.................................................. 11
5.2 The objective function .................................................................. 11
5.3 Parameter estimation.................................................................... 12
6. RESULTS AND DISCUSSION ................................................................ 13
6.1 Stock assessment......................................................................... 13
6.2 Retrospective analysis ................................................................. 17
6.3 Transition from the 2007 to the 2008 assessment ..................... 17
6.4 Harvest control rule application .................................................. 17
7. ACKNOWLEDGEMENTS ....................................................................... 20
8. REFERENCES ........................................................................................ 20
9. FIGURES................................................................................................. 22
10. APPENDIX: THE POPULATION DYNAMICS MODEL AND LIKELIHOOD MODEL............................................................................. 36
10.1 Basic dynamics ............................................................................. 36
10.2 Vulnerability................................................................................... 38
10.3 Catches .......................................................................................... 38
10.4 The likelihood function ................................................................. 39
Figure 4.1 T he calendar year catch-rate indices for the non-spawning (top) and s pawning
(bottom) blue grenadier fisheries (Haddon, 2008) in c omparison t o t he series for 2006 and 2007 ( Haddon, 2007) . ................................................................................................ 5
Figure 4.2 T he onboard l engths for years 2007, 2006 a nd a ll years combined. G reen represents retained f ish, br own a re discarded f ish a nd g rey (in 2007) are proportions of fish w here it was not possible to di stinguish be tween di scarded a nd r etained f ish. ........ 6
Figure 4.3 T he proportion di scarded-at-age from the non-spawning fishery for 2007............ 6 Figure 4.4. T he port-based c atch-weighted l ength f requencies for the non-spawning blue
grenadier fishery over years 2002-2007. .......................................................................... 7 Figure 4.5. T he catch-weighted l ength f requency for blue grenadier of the spawning sub-
fishery in y ears 2004-2007. .............................................................................................. 8 Figure 4.6. T he observed pr oportion c aught–at-age data for the non-spawning (left) and
spawning (right) sub-fisheries in 2007. ............................................................................ 8 Figure 9.1. T op pl ot: Annual landings of blue grenadier (obs) and e stimated by the base case
model (model). B ottom plot: Discards estimated f rom the ISMP (solid l ine) and ba se-case model estimated v alues (dashed l ine). N ote that the lines for the modelled spawning and non- spawning (model) landings overlay those of the observed ( obs) lines for each s ub-fishery. ....................................................................................................... 22
Figure 9.2. C atch-per-unit-effort (CPUE) calculated us ing a GLM to s tandardise CPUE from log-books (obs; Haddon, 2008) and t he base-case model estimated C PUE for the spawning fishery (top) and t he non-spawning fishery (bottom)..................................... 23
Figure 9.3. V ulnerability of blue grenadier to be ing caught (but not necessarily landed) by the two s ub-fisheries (top) and t he probability of being discarded i f caught (bottom) as a function of length c lass for the base case model. ........................................................... 24
Figure 9.4. O bserved ( bars) and m odel estimated ( lines) proportion c aught at age for the spawning sub-fishery and ba se case model. ................................................................... 25
Figure 9.5. O bserved ( bars) and m odel estimated ( lines) proportion c aught at age for the non-spawning sub-fishery and ba se case model. ............................................................ 26
Figure 9.6. O bserved ( bars) and m odel estimated ( lines) proportion di scarded-at-age for the non-spawning sub-fishery and ba se case model. ............................................................ 27
Figure 9.7. E stimated r ecruitment multipliers (the amount by which t he recruitment deviated from that predicted by the stock-recruit relationship) versus year of spawning for the base case model. B ottom: The median ( solid l ine), uppe r and l ower 95% bounds (dashed l ines) on t he recruitment multipliers for the base case model. ......................... 28
Figure 9.8. T he time-trajectory of female spawning biomass (left) and t otal spawning biomass (right) for the base case model. T he vertical lines show the estimates of spawning biomass derived f rom surveys of egg abundance in 1994 a nd 1995 a nd acoustic surveys from 2003 t o 2007. T he horizontal line shows Bref, w hich i s defined a s the average female spawning biomass over 1979–1988................................................. 29
Figure 9.9. T he trajectory of female spawning biomass relative to t he reference biomass, Bref for the base case model. T he horizontal lines show the 0.48 a nd 0.20 l evels. ....... 29
Figure 9.10. T he female spawning biomass (top) in r elation t o t he egg survey estimates of biomass and t he total spawning biomass (bottom) in r elation t o t he acoustic estimates for each of the base case (‘Low’) assessments from 2004 t o 2008. ............................... 30
Figure 9.11 The estimated a nnual recruitment multipliers for each of the base case assessments of blue grenadier from 2003 t o 2008. ......................................................... 31
Figure 9.12. T he female spawning biomass as a function of the data sources provided t o t he assessment. 2007 i s the series from the 2007 a ssessment (Tuck and P unt, 2007) , C = catch da ta series from 2008 i ncluded, C AA = updated a ge data are included, C PUE = updated c atch r ates series from 2008 i s included ( Haddon, 2008) . 2008 i s equivalent to C + CPUE + CAA + D + AC, w here AC is the inclusion of the 2007 a coustic biomass estimate ........................................................................................................................... 32
LIST OF FIGURES
Figure 9.13 The female spawning biomass relative to the reference biomass as a function of the data sources provided to the assessment. 2007 is the series from the 2007 assessment (Tuck and Punt, 2007), C = catch data series from 2008 included, CAA = updated age data are included, CPUE = updated catch rates series from 2008 is included (Haddon, 2008). 2008 is equivalent to C + CPUE + CAA + D + AC, where AC is the inclusion of the 2007 acoustic biomass estimate............................................................33
Figure 9.14. The trajectories of the landed RBC (top) and the corresponding depletion level (bottom) according to the 2 potential harvest control rules applied in the SESSF. The depletion figure also shows the depletion if a constant catch equal to the current catch of 4,368t is applied over all projected years. ..................................................................34
Figure 9.15 The trajectory of female spawning biomass relative to the reference biomass following the historic period and future projections under the two harvest control rules (20:40:40 and (20:35:48). ...............................................................................................35
LIST OF TABLES
Table 4.1. Landed and discarded catches for the winter spawning and non-spawning sub-fisheries by calendar year. These estimates have been adjusted scaled up to the SEF2 data (see text). The annual TAC is also shown. *Note that a voluntary industry reduction to 4,200 t was implemented in 2005.................................................................3
Table 4.2. Standardised CPUE (Haddon, 2007) for the spawning and non-spawning sub-fisheries by calendar year. ................................................................................................4
Table 4.3. The estimated biomass (tonnes) of blue grenadier on the spawning grounds in years 2003 to 2007 (Ryan and Kloser, 2008). ..................................................................9
Table 4.4. The age-reading error matrix, shown as the percentage of times an animal with true age given by the column header is aged to be of the age given by the rows. Source: A.E. Punt and Central Aging Facility (CAF, PIRVic, Queenscliff, Victoria)................10
Table 5.1. Parameter values assumed for some of the non-estimated parameters of the base-case model.......................................................................................................................12
Table 6.1. Estimated values for several parameters of interest. The base case model is shown as well as sensitivity tests. Results are shown for base-case runs in the previous 3 years for comparison with the 2008 assessment. ‘Curr’ refers to the current or final year of the estimation. The High Models use the higher acoustic survey estimates of total spawning biomass with the egg survey estimates of female spawning biomass doubled. The Low models use the lower acoustic estimates of total spawning biomass with the base-case egg survey estimates. Both of these models assume 2 times turnover. The 2008 base case model uses the Low model assumptions, assumes all fish less than 50cm were discarded in 2007 and assumes a cpue cv of 0.3...................................................15
Table 6.2. The estimated 2009 mid-year depletion and RBCs (landed and total; tonnes) for the base-case model for two Tier 1 harvest control rules with target biomass depletions of either 48% or 40%......................................................................................................19
Table 6.3. The time series of landed RBCs and corresponding depletions relative to Bref for each Tier 1 rule. Also shown is the annual depletion if the current landed catch of 4,368 t is maintained over all projected years. .........................................................................19
1 BLUE GRENADIER STOCK ASSESSMENT
1. SUMMARY
The 2008 assessment of blue grenadier Macruronus novaezelandiae uses the age-structured integrated assessment method developed by Punt et al. (2001). The assessment has been updated by the inclusion of data from the 2007 calendar year. In addition, age reading error and new biological parameters relating to the proportion spawning and the length at maturity, first introduced in August 2006, have been used. Estimates of spawning biomass from acoustic surveys from 2003-2007 (with 2 times turnover) and egg survey estimates of female spawning biomass from 1994-1995 (base-case estimates) are included. This corresponds to the ‘Low’ model of Tuck and Punt (2006; 2007) and is referred to as the base-case model here.
Results conclude that the female spawning biomass in 2007 is around 71% of the reference biomass and the depletion in 2009, used for the harvest control rules, will be approximately 50%. This compares with 47% for the 2006 depletion and 44% for the 2008 depletion in the 2007 assessment. The increases relative to the reference biomass between the 2007 and 2008 assessments are in part due to recent estimated biomasses being shifted upward through the increased level of the 2006 and 2007 acoustic estimate and the increased cpue in both sub-fisheries since 2005. The age data also suggests an increase in biomass. The marked decline in predicted biomass relative to the reference level over years 2007 and 2009 (from 0.71 to 0.50) is worth noting. This is likely to be due to the declining availability of the large cohort of the mid-1990s (as they senesce) and the majority of the catch being caught from the relatively smaller cohort of 2003/04
The Recommended Biological Catch (RBC) (landed catch and discards) for 2009 for the base-case model is 6,459 t (20:40:40) or 5,036 (20:35:48). The long-term RBCs are between 5,000 and 5,600 t. In comparison, the RBCs for 2008 from the 2007 assessment were between 3,300 t and 4,700 t, with long-term RBCs of around 5,500 t.
The 2008 assessment shows a further recruitment in 2006. The magnitude of this recruitment is uncertain and will become clearer as these fish move into the available biomass. The recruitments of 2003/04 and 2006 are estimated to be about twice that expected from the stock-recruitment relationship. While a positive sign for the stock and fishery following several years of poor recruitment, these recruitments are not estimated to be as large as the recruitments of the mid-1990s.
2. INTRODUCTION
An integrated analysis model has been applied to the blue grenadier stock of the Southern and Eastern Scalefish and Shark Fishery (SESSF), with data updated by inclusion of the 2007 calendar year data (catch and discard at age; updated catch rate series; landings and discard catch weight) and additional information from acoustic surveys of spawning biomass (series from 2003-2007). The same assessment model that has been used in previous years (e.g. Punt et al., 2001; Tuck and Punt, 2006; 2007) was used this year. This document presents (a) diagnostic plots and (b) recommended biological catches (RBCs) from an application of the Tier 1 harvest control rules.
2
The model considered here includes age-reading error (Punt, pers. comm.), updated biological parameters for the proportion spawning and length at maturity (for males and females) and an assumption of 2-times turnover on the spawning ground. The base-case egg survey estimates of female (only) spawning biomass for 1994 and 1995 are included. The acoustic estimates are assumed to pertain to total (male and female) spawning biomass. In Tuck and Punt (2006; 2007) two models were considered, differing according to the target strength used to produce the absolute estimates of spawning biomass from the acoustic surveys and assumptions about the egg survey estimates. The ‘High’ model assumes the target strength of Macauley (2004) and doubles the egg survey estimates. The survey estimates of absolute abundance used when fitting this model are higher than those used when fitting the ‘Low’ model which uses the Cordue (2000) target strength and the base-case egg survey estimates of spawning biomass. Following the recommendations of Ryan et al. (2007), here we only consider the ‘Low’ model (referred to as the base case model here), with the spawning biomass estimates resulting from the target strength estimates of Ryan and Kloser (2008).
3. THE FISHERY
Blue grenadier are found from New South Wales around southern Australia to Western Australia, including the coast of Tasmania. Data support the hypothesis of a single breeding population in Australian waters, however spawning fish have recently been caught off the east coast of Australia. Blue grenadier is a moderately long-lived species with a maximum age of about 25 years and an age at maturity of 4-5 years. Spawning occurs off western Tasmania between late May and early September. Adults migrate to the spawning area from throughout southeastern Australia, with large fish arriving earlier in the spawning season.
Blue grenadier are caught by demersal trawling. The global agreed TAC in 2007 was 3,530 tonnes (with an additional 583 t for 1 January to 30 April 2008) and in 2006 it was 3,730 tonnes. The annual TACs are show in Table 4.1. There are two defined sub-fisheries: the spawning and non-spawning fisheries. The non-spawning fishery catches have been relatively poor over the last few years, whereas the spawning fishery catches have shown a marked increase since the mid-1990s.
4. DATA
The model has been updated by the inclusion of the 2007 catch- and discard-at-age from the spawning and non-spawning fisheries; updated cpue series (Haddon, 2008), the total mass landed and discarded, mean length- and weight-at-age; updated acoustic estimates of spawning biomass (Ryan and Kloser, 2008) and estimates of the female spawning biomass in 1994 and 1995 from egg surveys (Bulman et al., 1999). Data were formulated by calendar year (i.e. 1 Jan to 31 Dec).
4.1 Catch
The landings from the SEF1 logbook data were used to apportion catches to the spawning and non-spawning fisheries. The SEF1 landings have been adjusted upwards to take account of
Year
3 BLUE GRENADIER STOCK ASSESSMENT
differences between logbook and landings data (multiple of 1.4 for the non-spawning fishery since 1986; 1.2 for the spawning fishery from 1986 up to and including 1996; D. Smith, pers. comm.). These figures were then scaled up to the SEF2 data. As SEF2 data were only available from 1993, for years prior to this the average scaling factor from 1993 to 1998 was used to scale the data. The landings data are provided in Table 4.1.
Table 4.1. Landed and discarded catches for the winter spawning and non-spawning sub-fisheries by calendar year. These estimates have been adjusted scaled up to the SEF2 data (see text). The annual TAC is also shown. *Note that a voluntary industry reduction to 4,200 t was implemented in 2005.
1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Landings Discards TAC
Spawning Non-spawning Spawning Non-spawning
245 245 410 410 225 225 390 390 450 450 675 675 600 600 321 1832 1020 2211 416 2254 47 2780 743 2543 830 3816 663 2384 990 2359 1196 1915 1196 1558 1465 1505 2957 1576 3283 2451 6106 3218 6037 2618 7670 1502 7417 1744 7504 986 4866 1785 2973 1732 2058 1798 1815 1641
10000 80 10000
975 10000 3716 10000 1329 10000 123 10000 69 10000 10 10000 2 10000 4 9000
37 7000 513 5000* 142 3730 13 3530
4.2 Catch rates
Haddon (2008) provides the updated catch rate series for blue grenadier (Table 4.2, Figure 4.1). Models 5 and 4 of Haddon (2008) were recommended for use in the assessment models for the
4
non-spawning and spawning fisheries respectively. Both series have declined in 2007 relative to 2006 but are still high compared to 2004 as a result of the large increases in 2005 and 2006.
Table 4.2. Standardised CPUE (Haddon, 2007) for the spawning and non-spawning sub-fisheries by calendar year.
Year Spawning Non-spawning
CPUE Records CPUE Records
1986 1.00 77 1.00 2838 1987 1.40 156 1.25 3357 1988 2.99 91 1.33 3914 1989 0.76 31 1.48 4274 1990 0.75 147 1.44 3490 1991 2.91 132 1.00 4543 1992 1.31 189 0.87 3579 1993 2.32 154 0.67 4192 1994 1.25 318 0.58 4485 1995 0.51 477 0.41 5065 1996 0.76 489 0.36 5351 1997 0.58 436 0.38 6097 1998 0.91 575 0.61 6596 1999 0.68 1044 0.64 8072 2000 0.71 931 0.46 7622 2001 1.15 1085 0.26 7177 2002 0.83 1024 0.27 6304 2003 0.80 1018 0.22 5650 2004 0.66 803 0.36 6390 2005 1.40 410 0.43 5323 2006 2.44 466 0.57 4330 2007 1.40 304 0.50 3652
5 BLUE GRENADIER STOCK ASSESSMENT
1.8 Non-spawning CPUE
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
2006 series 2007 series 2008 series
0 1985 1990 1995 2000 2005 2010
3.5 Spawning CPUE
0 1985 1990 1995 2000 2005 2010
0.5
1
1.5
2
2.5
3
2006 series 2007 series 2008 series
Figure 4.1 The calendar year catch-rate indices for the non-spawning (top) and spawning (bottom) blue grenadier fisheries (Haddon, 2008) in comparison to the series for 2006 and 2007 (Haddon, 2007).
4.3 Length Frequencies and Catch-at-age
The onboard length data for 2007, 2006 and all other years combined are shown in Figure 4.2. As it was not possible to distinguish between discard and retained lengths in 2007, it was assumed for the base-case model that all fish of length smaller than 50cm were discarded. The discards-at-age for 2007 are shown in Figure 4.3. A model sensitivity was considered where fish less than 70cm were assumed to have been discarded.
1.05
0.90 2007
0.75
0.60
0.45
0.30
0.15
0.00 0 2 4 6 8 10 12 14
ed-at-age from the non-spawning fishery for 2007.
1985-2005 n = 81012 onboard lf20000
Frequency
16000
12000
8000
4000
0 0 20 40 60 80 100 120 140
Length
Frequency
1000
2006 n = 7859 onboard lf
0 20 40 60 80 100 120 140
2000
0
Length
Frequency
2007 n = 893 onboard lf100
80
60
40
20
0 0 20 40 60 80 100 120 140
Length
6
Figure 4.2 The onboard lengths for years 2007, 2006 and all years combined. Green represents retained fish, brown are discarded fish and grey (in 2007) are proportions of fish where it was not possible to distinguish between discarded and retained fish.
Figure 4.3 The proportion discard
Catch-weighted length frequencies across ports were used to produce the non-spawning length frequencies used in this assessment (N. Klaer, pers. comm.; D. Smith, pers. comm.). Figure 4.4 shows recent year non-spawning length frequencies. The age-compositions over all years are shown in Figure 9.4 to Figure 9.6.
Spawning sub-fishery length frequencies for 2007 were obtained from AFMA on-board observations. To obtain the overall length-frequency, length records were catch-weighted by the weight of catch from the haul and the sample weight of the fish (Figure 4.5).
10 9 8 7 6 5 4 3 2 1 0
40 50 60 70 80 90 100 110 120 40 50 60 70 80 90 100 110 120
10 9 8 7 6 5 4 3 2 1 0
40 50 60 70 80 90 100 110 120 40 50 60 70 80 90 100 110 120
9
8
7
6
5
4
3
2
1
0
2002 Non-spawning 2005 Non-spawning
9
8
7
6
5
4
3
2
1
0
2006 Non-spawning 2003 Non-spawning
9
8
7
6
5
4
3
2
1
0
2004 Non-spawning 2007 Non-spawning
10
8
6
4
2
0 40 50 60 70 80 90 100 110 120 40 50 60 70 80 90 100 110 120
Figure 4.4. The port-based catch-weighted length frequencies for the non-spawning blue grenadier fishery over years 2002-2007.
7 BLUE GRENADIER STOCK ASSESSMENT
The catch-at-age for 2007 for each of the two sub-fisheries is shown in Figure 4.6. As expected, the non-spawning age composition shows the presence of a recent year-class progressing into the available biomass. This year-class has now entered the spawning fishery also.
5
4
3
2
1
0
50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120
6
5
4
3
2
1
0
2004 Spawning 2006 Spawning
5
4
3
2
1
0
2005 Spawning 2007 Spawning
5
4
3
2
1
0 50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120
Figure 4.5. The catch-weighted length frequency for blue grenadier of the spawning sub-fishery in years 2004-2007.
0.8
0.6
0.4
0.2
0.0 2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16
2007 2007
0.0
0.2
0.4
Figure 4.6. The observed proportion caught–at-age data for the non-spawning (left) and spawning (right) sub-fisheries in 2007.
8
4.4 Age-reading error
Standard deviations for aging error have been estimated, producing the age-reading error matrix of Table 4.4 (Punt, pers. comm.).
9 BLUE GRENADIER STOCK ASSESSMENT
4.5 Acoustic survey estimates
Estimates of spawning biomass for years 2003-2007 are provided in Ryan and Kloser (2008). Two models of target strength were used in the assessments of Tuck and Punt (2006; 2007), namely Macauley (2004) and Cordue (2000). However, following the recommendations of Ryan and Kloser (2008), only estimates based on their results are presented here.
Blue grenadier in-situ target strength (TS) measurements are being used to convert the peak industry acoustic survey results to biomass in Australian waters (Kloser et al. 2007). These measurements were supported by acoustic modelling of the blue grenadier swim bladder and a range of assumed school fish tilt angles. New Zealand target strength measurements of hoki (same species as blue grenadier) were reviewed and these were a factor of 5-7 lower than Australian in-situ results due to the assumptions of fish tilt orientation and species identification (Kloser at al. 2007). No evidence to support the hoki assumed tilt distribution or species identification was found in the blue grenadier experiments, but these lacked visual verification of targets. To resolve this, new measurements of blue grenadier were obtained in the winter of 2008 with an Acoustic-Optical system attached to the headline of a trawl net off the west coast of Tasmania (Ryan et al. 2008). In-situ TS values were made that had corresponding video and digital photos, removing any uncertainty regarding species identification. A preliminary assessment of these TS measures support earlier blue grenadier target strength results. Uncertainty regarding tilt orientation is being reviewed and investigated as part of the research project. Based on the evidence to date, our biomass results are based on blue grenadier in situ target strength measurements for ongoing blue grenadier peak biomass surveys.
Table 4.3 shows the spawning biomass estimates with their corresponding c.v. It is assumed that the spawning ground experiences a turnover rate equal to 2 (i.e. for the model applied here, the spawning biomass estimates are doubled).
Table 4.3. The estimated biomass (tonnes) of blue grenadier on the spawning grounds in years 2003 to 2007 (Ryan and Kloser, 2008).
2003 2004 2005 2006 2007 Spawning biomass (t)
c.v. used in assessment model 24,690
0.3 16,295 0.46
18,852 0.3
42,882 0.3
56,630 0.52
4.6 Egg survey estimates
Egg survey estimates of female spawning biomass are available for 1994 and 1995 (Bulman et al., 1999). The egg-estimates (cv) for 1994 and 1995 respectively are: 57,772 (0.18) and 41,409 (0.29). For the analysis considered here, the base-case egg estimates were used.
Table 4.4. The age-reading error matrix, shown as the percentage of times an animal with true age given by the column header is aged to be of the age given by the rows. Source: A.E. Punt and Central Aging Facility (CAF, PIRVic, Queenscliff, Victoria).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
88.6 11.4
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
12.2 75.5 12.2
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 13.1 73.8 13.1
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.1 13.9 72.0 13.9
0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.1 14.9 70.0 14.9
0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.1 15.9 68.0 15.9
0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.2 16.8 65.9 16.8
0.2 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.3 17.8 63.7 17.8
0.3 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.5 18.8 61.5 18.8
0.5 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7 19.8 59.1 19.8
0.7 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.9 20.7 56.8 20.7
0.9 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.3 21.5 54.4 21.5
1.3 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.7 22.3 52.0 22.3
1.7
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.2 23.0 49.6 25.2
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 2.9 23.5 73.6
10
11 BLUE GRENADIER STOCK ASSESSMENT
4.7 Parameters of breeding biology
The assessment models prior to 2006, including base-case models, have assumed that the proportion of females that spawn is 0.77 and that the length at maturity is 70cm (Punt et al., 2001). These values were taken from research on hoki in New Zealand (Livingston et al., 1997). Recent studies have provided more up-to-date values for these parameters that are specific to the Australian stock of blue grenadier (S. Russell and D. Smith, pers. comm.), namely 0.84 for the proportion of females that is on the spawning grounds, and lengths at 50% maturity of 63.7cm for females and 56.8cm for males. As no information was available on the proportion of non-spawning male blue grenadier, it was assumed that this proportion was the same as that for females. In the results that follow (as was the case in Tuck and Punt (2006; 2007)), the updated parameters have been used.
5. ANALYTIC APPROACH
5.1 The population dynamics model
The population and likelihood models applied in 2008 are the same as those used in the 2007 assessment and are based upon the integrated analysis model developed for blue grenadier in the South East Fishery by Punt et al. (2001; Appendix; see also Tuck and Punt, 2007). The 2008 model is updated and extended by including the following data:
• the total mass landed and discarded during 2007; the catch- and discard-at-age during 2007 and the estimated mean length and weight of each age-class present during 2007,
• revised standardised CPUE series, • an updated age-reading error matrix, • an acoustic estimate of the 2007 spawning biomass off western Tasmania.
Two sub-fisheries are included in the model – the spawning sub-fishery that operates during winter (June – August inclusive) off western Tasmania (zone 40), and the non-spawning sub-fishery that operates during other times of the year and in other areas throughout the year. The model is sex dis-aggregated. However, male and female fish are assumed to grow at the same rate.
Parameter uncertainty is examined through the use of sensitivity tests and by applying the Markov Chain Monte Carlo (MCMC) algorithm (Hastings, 1970; Gelman et al., 1995).
5.2 The objective function
The negative of the logarithm of the likelihood function includes five components. These relate to minimizing the sizes of the recruitment residuals, fitting the observed catches and discards by fleet, fitting the observed age-compositions by fleet, fitting the catch rate information, and fitting the estimates of spawner biomass from the egg and acoustic surveys. The Appendix has details of the likelihood formulations (see also Punt et al. (2001)).
12
5.3 Parameter estimation
The values assumed for some of the (non-estimated) parameters of the base case models are shown in Table 5.1. The model has 118 estimated parameters: 2 catchability coefficients; 1 female natural mortality, 1 B0, 31 annual fishing mortality rates for each of the two sub-fisheries; recruitment residuals for 28 years and 19 age classes in the first year; 2 selectivity parameters for the spawning sub-fishery and 3 for the non-spawning; and 2 parameters for the probability of discarding-at-length f unction.
The values for the parameters that maximize the objective function are determined using the AD Model Builder package1. This assessment quantifies the uncertainty of the estimates of the model parameters and of the other quantities of interest using Bayesian methods. The Markov Chain Monte Carlo (MCMC) algorithm (Hastings, 1970; Gelman et al., 1995) was used to sample 2000 equally likely parameter vectors from the joint posterior density function. The samples on w hich i nference is based w ere generated by running 2,000,000 c ycles of the MCMC algorithm, discarding the first 1,000,000 as a burn-in period and retaining every 500th parameter vector thereafter.
Table 5 .1. Parameter values assumed for some o f the n on-estimated parameters of the b ase-case m odel.
Parameter Description Value
N Weight for the catch- and di scard-at-age data 50 σ r c.v. f or the recruitment residuals 1.0 σ c c.v. f or the landings data 0.05 σd c.v. f or the discard da ta 0.3 σq c.v. f or the CPUE data 0.3 h “steepness” of the Beverton-Holt stock-recruit curve 0.9 x age of plus group 15 y ears µ fraction of mature population t hat spawn e ach y ear 0.84 l∞ von B ertalanffy parameter (maximum length) 102.76 c m κ von B ertalanffy parameter (growth r ate) 0.16 y -1 t0 von B ertalanffy parameter -2.209 y aa allometric length-weight equations 0.00375 g -1.cm bb allometric length-weight equations 3.013 lm length a t maturity (knife-edged) (M, F ) 63.7, 56.8c m
1 Copyright 1991, 1992 Otter Software Ltd.
13 BLUE GRENADIER STOCK ASSESSMENT
6. RESULTS AND DISCUSSION
6.1 Stock assessment
Figure 9.1 shows the observed and predicted fits to the landings and discards from each sub-fishery. The model is forced to fit the recorded landings because of the low c.v. that is assumed for these data (σc = 0.05, Table 5.1). The model is able to fit the recent drop in the mass of discards and the recent increase; however the large discard measured in 1997 is not well estimated despite the ability of the model to allow for density-dependant discarding.
The estimated natural mortality figure for females is approximately 0.171 and consequently that for males is 0.21 (as male natural mortality is assumed to be 1.2 times that of females). This compares with 0.165 and 0.2 in Tuck and Punt (2007).
For the winter spawning sub-fishery, Figure 9.2 shows that the model is not able to fit the early large fluctuations in the CPUE, nor the large increases in CPUE in years 2005, 2006 and 2007 Note that the 2007 catch rate has declined substantially from the 2006 value, but is still higher than catch rates from the mid-1990s to 2004. Previously, the model has been able to achieve a reasonable fit to the CPUE in those intermediate years, but it is now balancing its desire to fit to the lower catch rate years and the higher catch rates of the last 3 years.
The fit to the CPUE for the non-spawning sub-fishery consistently shows an inability to fit to the increased catch rates observed in the late 1990s. The model shows an increase (and decline) in catch rate after the observed catch rate increase (and decline). However, the modelled CPUE has begun increasing in line with the observed increases in 2005 and 2006. In general though, it appears the modelled non-spawning catch rate is 1 to 2 years out of phase with that observed. Attempts to provide better fits to the non-spawning fishery catch rates have not been fruitful (such as forcing fits to the catch rate by lowering the cv). This issue will be explored further as a high priority. Changes to the form of the selectivity function may prove successful and conversion of the model to SS2 may assist this exploration.
The estimated vulnerability of fish of a given length class to being caught (but not necessarily landed) by either sub-fishery is shown in Figure 9.3. The probability that a fish will be discarded once it has been caught is also shown.
The fits to the catch-at-age and the discard-at-age data for both sub-fisheries are reasonably good across all years (Figure 9.4 and Figure 9.6). The catch ate age data for 2007 however shows a lack of fit; underestimating 4 and 13 year olds and over-estimating 3 year olds. A comparison of the age-length keys (ALKs) in 2006 and 2007 shows that there were many fish aged as 2 year olds in 2006. These fish do not appear in as high a proportion as 3 year olds in the 2007 ALK. This is because the birth date for blue grenadier is 1 June. In 2007, blue grenadier were not collected for ageing until after 1 June 2007. As such, all of the fish of ages 2 and 3 in 2006 (from the same cohort) are aged as 4 year olds in 2007 (K. Krusic-Golub, pers. comm.). Further exploration of assessment models with a biological year should be considered in order to overcome this issue.
Figure 9.7 shows the estimated annual recruitment multipliers, and illustrates a long period of poor recruitment following the strong recruitments of 1994 and 1995. An increase in
14
recruitment has been estimated for years 2003, 2004 and 2006. These recent recruitment events are approximately 2 to 3 times that predicted by the stock recruitment relationship. The recruitments do not appear to be as strong as those of the mid-1990s. Given the smaller number of onboard samples taken in 2007, the magnitude and potential of the most recent estimated recruitment (2006) will become clearer over the next few years as it enters the commercial fishery.
Table 6.1 shows the results against various quantities of interest for the base case models. The
quantities of interest shown are the estimated pristine female spawning biomass ( B0 ); the
reference biomass ( Bref ) which is the average female spawning biomass over 1979–1988; the ~ ~
spawning biomass in 1979 ( B79 ) and in 2007 ( B2007 ) and its size in 2007 relative to the ~
reference level (depletion, B / B ); the estimated fishing mortality rate for the spawning y ref
( F 1 ) and non-spawning ( F 2 ) sub-fisheries for 2007 (=curr); the estimated recruitment curr curr
residual for the strong 1994 cohort, and the more recent 2004 cohort, and the negative log
likelihood (-ln L) value from the model. Also shown are the base-case results for previous
years’ assessments. Note that the final year of biomass estimation (curr) is one year less than
the year the assessment is produced.
The assessment of 2008 concludes that the reference female biomass is approximately 45,500 t and that current female spawner biomass (in the middle of 2007) is approximately 71% of the reference biomass. Figure 9.8 shows the spawning biomass trajectory with the egg survey estimates (left; female spawning biomass only) and the acoustic estimates (right; total spawning biomass). Intervals on survey estimates are 2 standard deviations. Figure 9.9 shows the female spawning biomass trajectory relative to the reference biomass for each model. The trend in relative spawning biomass is similar to those seen in previous assessments; however, there is an increase in the most recent 2 years that was not predicted in the 2007 assessment (see below).
Specification B0 Bref ~ B 79
~ B curr
~ B curr / B ref
1 F curr2 F curr R 94 R 03 -ln L
Previous assessment results
Base-case, curr=2002 33026 52605 51685 31241 59.39% 0.175 0.027 6.0 - 352.42 Base-case, curr=2003 26877 42082 41441 18066 42.93% 0.278 0.026 6.2 - 362.06 Base-case, curr=2004 30241 48612 47311 21283 43.78% 0.139 0.036 6.9 0.71 396.00
2006 assessment,
curr=2005 Low Model 27467 49293 47396 18065 36.65% 0.085 0.067 11.4 1.7 372.67 High Model 63917 148749 155947 62203 41.82% 0.027 0.020 10.1 1.8 378.56
2007 assessment,
curr=2006 Low Model 30340 50644 44701 23867 47.13% 0.050 0.055 11.6 2.1 466.49 High Model 69677 140254 130565 75166 53.59% 0.016 0.019 10.2 2.0 466.40
2008 assessment,
curr=2007 Base case model 29023 45493 39963 32423 71.3% 0.039 0.037 13.1 2.8 524.76
Discard all < 70cm 26954 43953 38323 32847 74.7% 0.038 0.038 13.9 3.5 546.82 Cpue cv=0.15 35249 64690 56705 42478 65.6% 0.030 0.026 11.0 2.8 727.10
Half age Weight 31334 47460 40790 35092 73.9% 0.037 0.032 11.8 2.5 337.84
15 BLUE GRENADIER STOCK ASSESSMENT
Table 6.1. Estimated values for several parameters of interest. The base case model is shown as well as sensitivity tests. Results are shown for base-case runs in the previous 3 years for comparison with the 2008 assessment. ‘Curr’ refers to the current or final year of the estimation. The High Models use the higher acoustic survey estimates of total spawning biomass with the egg survey estimates of female spawning biomass doubled. The Low models use the lower acoustic estimates of total spawning biomass with the base-case egg survey estimates. Both of these models assume 2 times turnover. The 2008 base case model uses the Low model assumptions, assumes all fish less than 50cm were discarded in 2007 and assumes a cpue cv of 0.3.
17 RESULTS AND DISCUSSION
6.2 Retrospective analysis
Figure 9.10 and Figure 9.11 show the female spawning biomass, total spawning biomass and recruitment multipliers for each of the assessments from 2004 to 2008. This shows how the 2008 spawning biomass trajectories have increased in recent years compared to previous assessments. This is due to the increase in observed catch rate, the age data and the large 2006 acoustic estimate (Tuck and Punt, 2007).
6.3 Transition from the 2007 to the 2008 assessment
To explore the changes observed in Figure 9.10 and Figure 9.11 following the inclusion of the 2007 calendar year data, a sequential analysis was conducted to determine the influence of each of the input data sources. Figure 9.12 show the SSB time series as each data source (listed and labelled below) is added and an assessment conducted. Note that the age data below refers to the catch-at-age, discard-at-age, mean length-at-age and age-reading error data. The various transitional assessments and their data-source changes are:
1. The 2007 assessment result (2007)
2. The 2007 assessment data with the addition of the updated catches, including 2007 (2007 C)
3. Option 2 with the updated catch rate series of 2008 (C + Cpue)
4. Option 2 with the addition of the age data (C + Age Data)
5. Option 4 with the addition of the cpue data (C + Cpue + Age Data)
6. Option 5 with the addition of the updated discard masses (C + Cpue + AgeData + D)
7. The 2008 assessment result (2008)
Note that the 2008 assessment result is equivalent to (C + Cpue + AgeData + D + AC), where AC is the acoustic estimates of spawning biomass.
Figure 9.12 and Figure 9.13 show that, as each data source is added, the most recent year female spawning biomass changes from the 2007 assessment values through to the 2008 assessment values. The inclusion of the ageing data and cpue produces a substantial upward shift in the trajectory. The updated acoustic data do not greatly influence the time series due to the large error bounds on the 2007 biomass estimate.
6.4 Harvest control rule application
The steps involved in computing the Recommended Biological Catch for 2007 using the Tier 1 rules are:
18
1. Determine the relationship between exploitation rate and spawning biomass, where the relative exploitation rates among the fleets are based on the exploitation rates estimated for 2008.
2. Find the exploitation rates so that spawning biomass is a pre-specified fraction of that in an unfished state.
3. Determine the depletion of the spawning biomass in the middle of 2009. 4. Determine the correction factor (if needed), and multiply the exploitation rates
calculated at step 2 by this correction factor. 5. Multiply the numbers-at-age in the middle of 2009 by the exploitation rates calculated
at step 4.
Two variants of the Tier 1 rules are applied depending on specifications for the target spawning biomass and the depletion at which the exploitation rate begins to be reduced to zero (all variants set the exploitation rate to zero if the stock is assessed to be depleted to below 20% of Bref):
a) 20-35-48; a target stock size of 48% of Bref, with the exploitation rate dropping off once the stock drops below 0.35 Bref.
b) 20-40-40; a target stock size of 40% of Bref, with the exploitation rate dropping off once the stock drops below the target level.
The mid-year depletion in 2009 must be calculated to apply the Tier 1 harvest control rule. The 2009 depletion is shown in Table 6.2 and is calculated by assuming a 2008 catch of 4,368 t. The resulting landed and total Recommended Biological Catches (RBC) for 2009 are given in Table 6.2.
The time series of landed RBCs and depletions under each Tier 1 rule is given in Table 6.3, Figure 9.14 and Figure 9.15. Note that the final depletions are not exactly 40% and 48% of Bref
.This occurs presumably because density-dependence in the stock recruitment model is a function of depletion relative to B0 and not relative to Bref. As a result the depletion in terms of B0 is higher than in terms of Bref. The annual depletion levels under the 2008 catch of 4,368t are also shown in this table. From Figure 9.15 it is worth noting the marked decline in biomass relative to the reference level over years 2007 and 2009 (from 0.71 to 0.50). This is likely to be due to the declining availability of the large cohort of the 1990s (as they senesce; Figure 9.4) and the majority of the catch being caught from the relatively smaller cohort of 2003/04.
From Table 6.3, the long-term RBCs are approximately 4,700t for a target depletion of 48% of the reference biomass and 5,270t for 40% (note these values are approximate as they have not stabilised over the 20 year projection horizon considered in Table 6.3).
19 RESULTS AND DISCUSSION
Table 6.2. The estimated 2009 mid-year depletion and RBCs (landed and total; tonnes) for the base-case model for two Tier 1 harvest control rules with target biomass depletions of either 48% or 40%.
Tier rule 2009 Landed Total RBC Depletion RBC (landed+discard)
20:40:40 0.50 6,089 6,459 20:35:48 0.51 4,750 5,036
Table 6.3. The time series of landed RBCs and corresponding depletions relative to Bref for each Tier 1 rule. Also shown is the annual depletion if the current landed catch of 4,368 t is maintained over all projected years.
2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027
Landed RBC Depletion 20:40:40 20:35:48 20:40:40 20:35:48 Ccurr=4,368
4367 4367 0.60 0.60 0.60 6089 4750 0.50 0.51 0.51 6027 4812 0.53 0.55 0.56 5882 4795 0.51 0.54 0.55 5823 4833 0.50 0.54 0.56 5757 4855 0.48 0.53 0.56 5646 4821 0.47 0.53 0.56 5558 4794 0.46 0.52 0.56 5491 4772 0.46 0.52 0.57 5439 4756 0.45 0.52 0.57 5399 4743 0.45 0.52 0.57 5368 4734 0.44 0.52 0.57 5344 4727 0.44 0.51 0.58 5325 4721 0.44 0.51 0.58 5311 4716 0.44 0.51 0.58 5299 4713 0.44 0.51 0.58 5290 4710 0.44 0.51 0.58 5283 4707 0.44 0.51 0.58 5277 4705 0.43 0.51 0.58 5272 4704 0.43 0.51 0.58
20
7. ACKNOWLEDGEMENTS
Many thanks are due to Sandy Morison, Andre Punt and all of the SS2-WG for their assistance with model discussions and development. Malcolm Haddon is thanked for providing catch rate indices, Mike Fuller and Neil Klaer for their advice on data matters. Kyne Krusic-Golub (Central Aging Facility) and the AFMA observer section are thanked for providing the aging data and spawning length frequency data respectively.
8. REFERENCES
Bulman, C. M., Koslow, J. A., and Haskard, K. A. 1999. Estimation of the spawning stock biomass of blue grenadier (Macruronus novaezelandiae) off western Tasmania based upon the annual egg production method. Marine and Freshwater Research. 50:197-207.
Francis, R.I.C.C. 1992. Use of risk analysis to assess fishery management strategies: a case study using orange roughy (Hoplosethus atlanticus) on the Chatham Rise, New Zealand. Canadian Journal of Fisheries and Aquatic Sciences 49: 922-930.
Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. 1995. Bayesian Data Analysis. Chapman and Hall, London.
Haddon, M. 2007. Standardized Commercial Catch-Effort data for selected Shelf and Slope Assessment Group Species for 1986 - 2006. Technical paper presented to the Slope Resource Assessment Group. July 23-24, 2007, Queenscliff, Victoria.
Haddon, M. 2008. Catch Rate Standardizations 2008 (for data 1986 – 2007). Technical paper presented to Slope Resource Assessment Group. 17-18 November 2008. Hobart, Tasmania.
Hastings, W.K. 1970. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57: 97–109.
Kloser R.J., Ryan T.E. and Geen, G. 2007. Development of a sustainable industry-based acoustic observation system for blue grenadier at the primary spawning sites. Report to Australian Fisheries Management Authority (AFMA).
Livingston, M.E., Vignaux, M. and Schofield, K.A. 1997. Estimating the annual proportion of non-spawning adults in New Zealand hoki, Macruronus novaezelandiae. Fishery Bulletin (US) 95:99-113.
McAllister, M.K., Pikitch, E.K., Punt, A.E., and Hilborn, R. 1994. A Bayesian approach to stock assessment and harvest decisions using catch-age data and the sampling/importance resampling algorithm. Canadian Journal of Fisheries and Aquatic Sciences 51: 2673-2687.
21 REFERENCES
Punt, A.E., Smith, D.C., Thomson, R.B., Haddon, M., He. X and Lyle, J.M. 2001. Stock assessment of the blue grenadier Macruronus novaezelandiae resource off south eastern Australia. Marine and Freshwater Resources. 52:701-717.
Ryan, T.E. and Kloser, R.J. 2008. Industry based acoustic surveys of Tasmanian West Coast blue grenadier during the 2007 spawning season. Australian Fisheries Management Authority. August 2008. Project 2006/832.
Ryan, T.E., Kloser, R.J and Geen, G. 2007. Industry based acoustic surveys of Tasmanian West Coast blue grenadier during the 2006 spawning season. Final report to AFMA. Project 2006/808.
Ryan, T.E., Kloser, R.J., and Macaulay, G.J. 2008. Visually verified in situ target strength measurements of fish using an acoustic-optical system attached to a trawl net. ICES Symposium on the Ecosystem Approach with Fisheries Acoustics and Comlementary Technologies, Bergen, Norway June 2008
Tuck, G.N. 2006. Updated stock assessment for blue grenadier in the Southern and Eastern Scalefish and Shark Fishery: July 2006. Report to the Slope Resource Assessment Group. 24-25 July 2006.
Tuck, G.N., Koopman, M. 2005. Updated stock assessment for blue grenadier in the South East Fishery, August 2005. Report to the Slope Resource Assessment Group. 25-26 August 2005.
Tuck, G.N., Punt, A.E. 2006. Updated stock assessment of blue grenadier Macruronus novaezelandiae based on data up to 2005: application of new base-case models, harvest control rules and decision analysis. Report to the Slope Resource Assessment Group. 25 August 2006.
Tuck, G.N., Punt, A.E. 2007. Updated stock assessment of blue grenadier Macruronus novaezelandiae based on data up to 2006: July 2007. Report to the Slope Resource Assessment Group. 25 August 2006.
Tuck, G.N., Smith, D.C and Talman, S. 2004. Updated stock assessment for blue grenadier in the South East Fishery, August 2004. Report to the Slope Resource Assessment Group. August 2004.
Dis
card
s (t
onne
s)
Land
ings
(to
nnes
)
10000
8000
6000
4000
2000
0 1980 1985 1990 1995 2000 2005
Spawning (obs) Spawning (model) Non-spawning (obs) Non-spawning (model)
10000
1000
100
10
1 1996 1998 2000 2002 2004 2006
Year
22
9. FIGURES
Figure 9.1. Top plot: Annual landings of blue grenadier (obs) and estimated by the base case model (model). Bottom plot: Discards estimated from the ISMP (solid line) and base-case model estimated values (dashed line). Note that the lines for the modelled spawning and non-spawning (model) landings overlay those of the observed (obs) lines for each sub-fishery.
FIGURES 23
0
1
2
3
4
5
6
CP
UE
Spawning (obs)
Spawning (est)
1985 1990 1995 2000 2005
1985 1990 1995 2000 2005 0
0.5
1
1.5
2
2.5
3
CP
UE
Non-spawning (obs)
Non-spawning (est)
Figure 9.2. Catch-per-unit-effort (CPUE) calculated using a GLM to standardise CPUE from log-books (obs; Haddon, 2008) and the base-case model estimated CPUE for the spawning fishery (top) and the non-spawning fishery (bottom).
Dis
card
pro
babi
lity
1
0 0 20 40 60 80 100
Length Class
24
Vul
nera
bilit
y
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Spawning Non-spawning
0 20 40 60 80 100
Length Class
Figure 9.3. Vulnerability of blue grenadier to being caught (but not necessarily landed) by the two sub-fisheries (top) and the probability of being discarded if caught (bottom) as a function of length class for the base case model.
Pro
port
ion
Pro
port
ion
Pro
port
ion
Pro
port
ion
Pro
port
ion
Pro
port
ion
Pro
port
ion
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
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0.5
0.4
0.3
0.2
0.1
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0.5
0.4
0.3
0.2
0.1
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0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
0.0
1999
1985
1994
1993
1992
1988 1998
1997
1984 Observed Model
2000
2001
2003 1996
2004
2005
2006
2007
Age
2 4 6 8 10 12 14 16
0.5
0.4
0.3
0.2
0.1
0.0
1995 2002
2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16
Age Age
Figure 9.4. Observed (bars) and model estimated (lines) proportion caught at age for the spawning sub-fishery and base case model.
FIGURES 25
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
0.0
0.5
0.4
0.3
0.2
0.1
0.0
1984
Observed Model
1994 2001
1985 1995 2002
1987 1996 2003
1988 1997 2004
1989 1998 2005
1992 1999 2006
0.5
0.4
0.3
0.2
0.1
0.0
1993 2000 2007
2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16
Age Age Age
Figure 9.5. Observed (bars) and model estimated (lines) proportion caught at age for the non-spawning sub-fishery and base case model.
Pro
port
ion
Pro
port
ion
Pro
port
ion
Pro
port
ion
Pro
port
ion
Pro
port
ion
Pro
port
ion
26
1996
0.00
0.15
0.30
0.45
0.60
Observed Model
2004
0.00
0.15
0.30
0.45
0.60
0.75
0.90
1.05
1997
0.00
0.15
0.30
0.45
0.60 2005
0.00
0.15
0.30
0.45
0.60
0.75
0.90
1.05
1999
0.00
0.15
0.30
0.45
0.60
1998
0.00
0.15
0.30
0.45
0.60
2006
0.00
0.15
0.30
0.45
0.60
0.75
0.90
1.05
2007
0.00
0.15
0.30
0.45
0.60
0.75
0.90
1.05
0 2 4 6
Age
8 10 12 14
0 2 4 6
Age
8 10 12 14
Figure 9.6. Observed (bars) and model estimated (lines) proportion discarded-at-age for the non-spawning sub-fishery and base case model.
2000
0.00
0.15
0.30
0.45
0.60
FIGURES 27
R
ecru
itmen
t mul
tiplie
r R
ecru
itmen
t mul
tiplie
r 14
13
12
11
10
9
8
7
6
5
4
3
2
1
0 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004
Year spawned
19 18 17 16 15 14 13 12 11 10
9 8 7 6 5 4 3 2 1 0 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004
Year spawned
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
28
Figure 9.7. Estimated recruitment multipliers (the amount by which the recruitment deviated from that predicted by the stock-recruit relationship) versus year of spawning for the base case model. Bottom: The median (solid line), upper and lower 95% bounds (dashed lines) on the recruitment multipliers for the base case model.
Fem
ale
spaw
ning
bio
mas
s
Acoustic - low, Egg - base case Acoustic - low, Egg - base case
90000 250000 80000
70000
60000
50000
40000
30000
20000
10000
0
Tot
al s
paw
ning
bio
mas
s
200000
150000
100000
50000
0 1978 1983 1988 1993 1998 2003 2008 1978 1983 1988 1993 1998 2003 2008
Figure 9.8. The time-trajectory of female spawning biomass (left) and total spawning biomass (right) for the base case model. The vertical lines show the estimates of spawning biomass derived from surveys of egg abundance in 1994 and 1995 and acoustic surveys from 2003 to 2007. The horizontal line shows Bref, which is defined as the average female spawning biomass over 1979–1988.
FIGURES 29
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1978 1983 1988 1993 1998 2003 2008 Fem
ale
spaw
ning
B r
elat
ive
to B
ref
Figure 9.9. The trajectory of female spawning biomass relative to the reference biomass, Bref for the base case model. The horizontal lines show the 0.48 and 0.20 levels.
Acoustic - low, Egg - base case T
otal
spa
wni
ng b
iom
ass
Fem
ale
spaw
ning
bio
mas
s 90000
80000
70000
60000
50000
40000
30000
20000
10000
0 1978 1983 1988 1993 1998 2003 2008
2007 2006 2005 2004 2008
250000
200000
150000
100000
50000
0
Acoustic - low, Egg - base case
1978 1983 1988 1993 1998 2003 2008
2007 2006 2005 2004 2008
Figure 9.10. The female spawning biomass (top) in relation to the egg survey estimates of biomass and the total spawning biomass (bottom) in relation to the acoustic estimates for each of the base case (‘Low’) assessments from 2004 to 2008.
30
FIGURES 31
0
2
4
6
8
10
12
14 R
ecru
itmen
t mul
tiplie
r 2004
2005
2006
2007
2008
1969 1979 1989 1999
Figure 9.11 The estimated annual recruitment multipliers for each of the base case assessments of blue grenadier from 2003 to 2008.
80000
70000
60000
50000
40000
30000
20000
10000
0
1978 1983 1988 1993 1998 2003 2008
2007 2008 2007 + C C + CAA C + CPUE C + CPUE + CAA C + CPUE + CAA + D
Fem
ale
spaw
ning
bio
mas
s
32
Figure 9.12. The female spawning biomass as a function of the data sources provided to the assessment. 2007 is the series from the 2007 assessment (Tuck and Punt, 2007), C = catch data series from 2008 included, CAA = updated age data are included, CPUE = updated catch rates series from 2008 is included (Haddon, 2008). 2008 is equivalent to C + CPUE + CAA + D + AC, where AC is the inclusion of the 2007 acoustic biomass estimate
FIGURES 33
1.6
1.4
1.2 ss
om
a
1
0.8
Fem
ale
spaw
ning
bi
0.6
0.4
0.2
0 1978 1983 1988 1993 1998 2003 2008
2007 2008 2007 + C C + CAA C + CPUE C + CPUE + CAA C + CPUE + CAA + D
.
Figure 9.13 The female spawning biomass relative to the reference biomass as a function of the data sources provided to the assessment. 2007 is the series from the 2007 assessment (Tuck and Punt, 2007), C = catch data series from 2008 included, CAA = updated age data are included, CPUE = updated catch rates series from 2008 is included (Haddon, 2008). 2008 is equivalent to C + CPUE + CAA + D + AC, where AC is the inclusion of the 2007 acoustic biomass estimate.
7000
6000
5000
Land
ed R
BC
(t)
4000
3000
2000
1000
0 2006 2011 2016 2021 2026
20:40:40 20:35:48
Dep
letio
n
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00 2006 2011 2016 2021 2026
20:40:40 20:35:48 Ccurr = 4,368
34
Figure 9.14. The trajectories of the landed RBC (top) and the corresponding depletion level (bottom) according to the 2 potential harvest control rules applied in the SESSF. The depletion figure also shows the depletion if a constant catch equal to the current catch of 4,368t is applied over all projected years.
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030
20:35:48 20:40:40
Figure 9.15 The trajectory of female spawning biomass relative to the reference biomass following the historic period and future projections under the two harvest control rules (20:40:40 and (20:35:48).
FIGURES 35
36
10. APPENDIX: THE POPULATION DYNAMICS MODEL A ND LIKELIHOOD M ODEL
The equations presented i n t his appendix ha ve been a dapted f rom those in P unt et al. (2001).
10.1 Basic dynamics
The dynamics of animals of sex s aged 1 a nd a bove are governed by the equation:
N s
y+1,1 if a = 1
−Z s
N s s y ,a −1
y +1,a = N y ,a −1e if 1 < a < x (A.1) N s e
−Z s y , x + N s e
−Z s y , x −1 if a = x
x y ,x−1 y ,
where N s y , a is the number of fish of sex s and age a at the start of year y (where y runs from
1 t o t),
Z s y ,a is the total mortality on f ish of sex s and a ge a during year y:
Z sy = M s 2,a + S 1 1 + 2
a F y Sa F y (A.2)
M s is the (age-independent) rate of natural mortality for animals of sex s,
S f y ,a is the vulnerability by s ub-fishery f (f=1 f or the ‘spawning’ sub-fishery, a nd f=2
for the ‘non-spawning’ sub-fishery) on f ish of age a during year y,
F f y is the fully-selected f ishing mortality by sub-fishery f during year y, a nd
x is the maximum age-class (taken t o be a plus-group). The number of 1-year-olds of sex s at the start of year y+1 i s related t o t he spawner biomass of females in t he middle of the preceding year according to t he equation:
s = [ ~ N y+1,1 0.5 B y /( α + β ~
B y )]e ε y (A.3)
where ~ By is the spawner biomass of females in the middle of year y:
x B% y =µ∑f w N f
−Z fy , a / 2
y ,a y ,a y ,a e (A.4) a=1
is the proportion of mature females that spawn e ach y ear,
37 APPENDIX
f y ,a is the proportion of females of age a that are mature during year y:
1 if L ≥ 70cm f = y,a
y , a 0 otherwise
w y ,a is the mass of a fish of age a in t he middle of the year y,
L y ,a is the mean length of a fish of age a during year y (given e ither by the empirical
mean length-at-age each year, or from the fit of a von Bertalanffy growth curve),
α, β are the parameters of the stock-recruitment relationship, a nd
ε y is the recruitment residual for year y (for ease of presentation, exp( ε y ) will be
referred t o a s the recruitment anomaly for year y).
The values for α and β are determined f rom the steepness of the stock-recruitment relationship (h) and t he virgin bi omass (B0) using the equations of Francis (1992). T he assumption t hat maturity is knife-edged a t 70 c m is very crude and a research pr oject has been pr oposed t o provide a more realistic picture of maturity as a function of length. I n pr inciple, t he probability of being mature-at-length c ould ha ve been a ssumed t o be the same as vulnerability to t he ‘spawning’ sub-fishery. T his assumption ha s been m ade for assessments of blue grenadier in New Zealand ( e.g. M cAllister et al., 1994) . H owever, i t may be substantially in e rror for blue grenadier in A ustralia because it is known t hat fish of different sizes arrive on t he spawning grounds at different times, a nd t hat some immature fish a re caught during the ‘spawning’ sub-fishery.
The specifications for the numbers-at-age at the start of 1979 a re based on t he assumption t hat the stock would ha ve been c lose to i ts unexploited e quilibrium size at that time:
R − a−1)M s
0 eε e ( a
s if a < xN1979,a = 0.5 (A.5)
R e−( x−1)M s
0 /(1− e−M s ) if a = x
where R 0 is the expected number of 1-year-olds at unexploited equilibrium (the sex ratio
at age 1 i s taken t o be 1:1), a nd
ε a is the recruitment residual for age a.
The equation f or the plus-group doe s not include a contribution by a recruitment residual because this group c omprises several age-classes, w hich w ill largely damp out the impact of inter-annual variation i n y ear-class strength.
38
10.2Vulnerability
The vulnerability of the gear is governed by a logistic curve that permits the probability of capture to drop off with length:
f f f f −ln19(Ly ,a −L50 ) /( L95 −L50 ) −1 if L ≤ L f (1+ e ) y ,a 95
S = (A.6) y ,a f f f f f−ln19(Ly ,a −L50 ) /( L95 −L50 ) −1 −λ ( Ly ,a −L95 ) otherwise (1+ e ) e
where L50 f is the length-at-50%-vulnerability for sub-fishery f,
L95 f is the length-at-95%-vulnerability for sub-fishery f, and
λ f is the “vulnerability slope” for sub-fishery f.
The vulnerability pattern for the ‘spawning’ sub-fishery is assumed to be asymptotic (i.e. λ = 0 for the ‘spawning’ sub-fishery).
10.3Catches
ˆ fThe catch (in number) of fish of age a by sub-fishery f during year y, C , and the number of y,aˆfish of age a discarded by sub-fishery f, during year y, D f , are given by the equations: y ,a
ˆ f (1− Py ,a ) Syf ,a Fy
f s −Z y
s ,aCy ,a = ∑ Z s N y ,a (1− e ) (A.7a)
s y ,a
~ P S f F f f y ,a y ,a y s −Z y ,aD = ∑ s N y ,a (1− e
s
) (A.7b) y ,a Zs y ,a
where P is the probability of discarding a fish of age a during year y:y ,a
s φ s ' φγ (∑ N y ,1 ) / max( ∑ N y ',1 ) (A.8) y '
s s 'P = y a −(La −L50 ) / δ,1+ e
D
γ is the maximum possible discard rate for the largest year-class,
LD 50 is the length at which discarding is half the maximum possible rate,
δ is the parameter that determines the width of the relationship between length and the discard probability, and
φ is the parameter that controls the extent of density-dependent discarding.
The rate of discarding is therefore assumed to be related only to the size of the year-class at birth; the impact of density-dependence on the rate of discarding is assumed to be constant
The summation in Equation (A.11) runs to x-1 and t-1 because the plus-group (age x) is not impacted by variability in year-class strength, and because the model is not used to predict the number of 1-year-olds for year t+1.
39 APPENDIX
during the whole of an animal’s life. The first assumption will be violated to some extent because inter alia the rate of discarding will depend on the abundance of other year-classes in the population (through high-grading). Violation of the second assumption is probably inconsequential because for older ages the form of the denominator of Equation (A.8) will mean that Py a ≈ 0 . ,
The model estimates of the catch (in mass) by sub-fishery f during year y, C yf , and of the mass
ˆof fish discarded by sub-fishery f during year y, Dyf , are given by the equations:
ˆ fx
ˆ fC = ∑w C (A.9a) , y a ,y y a a=1
f fD = ∑ x
w D (A.9b) , y a ,y y a a=1
Equations (A.9a) and (A.9b) imply that the (expected) mass of a fish of age a that is discarded is the same as the (expected) mass of a fish of age a that is retained.
10.4The likelihood function
The negative of the logarithm of the likelihood function includes five contributions. These relate to minimising the sizes of recruitment residuals, fitting the observed catches / discards by fleet, fitting the observed catch / discard age-compositions, fitting the catch rate information, and fitting the estimates of spawner biomass from the egg-production method.
5
L = ∑ Li (A.10) i=1
The contribution of the recruitment residuals to the negative of the logarithm of the likelihood function is based on the assumption that the inter-annual fluctuations in year-class strength are
2independent and log-normally distributed with a CV of σ r :
x−1 t−1 1 2 2L1 =
2σ 2 ∑ε a + ∑ε y
(A.11) r a=1 y=1
The contribution of the observed catch (in mass) information to the negative of the logarithm of the likelihood function is based on the assumption that the errors in measuring the catch in mass are log-normally distributed with a CV of σ c :
t 1 f ,obs f 2L2 = 2 ∑∑ (lnCy − lnC
y ) (A.12) 2σ c f y=1
f ,obs where Cy is the observed catch (in mass) by sub-fishery f during year y.
The contribution of the observed mass of discards to the negative of the logarithm of the ˆ f ˆ f f ,obs likelihood function follows Equation (A.12) except that C is replaced by D , C is y y y
2
40
replaced by the observed mass of discards by sub-fishery f during year y, and the summations over year are restricted to those years for which estimates of discards are available.
The contribution of the age composition information to the negative of the logarithm of the likelihood function is based on the assumption that the age-structure information is determined from a random sample of N animals from the catch:
15 + f ,obs fL3 = −∑∑∑ N ρ y ,a ln(ρ y ,a ) (A.13)
f y a =1
f ,obs where ρ is the observed proportion which fish of age a made up of the catch during year y ,a
y by sub-fishery f,
ρ yf ,a is the model-estimate of the proportion which fish of age a made up of the
catch during year y by sub-fishery f: x
f ˆ f ˆ fρ y ,a = ∑ χa,a" Cy ,a" / ∑Cy ,a ' (A.14) a" a '=1
χ is the probability that an animal of age a’ will be found to be age a (the age-a ,a '
reading error matrix).
Note that all animals aged 15 and older are treated as a single “age-class” when fitting to the catch proportion-at-age information. This prevents data for older fish (for which there is relatively little data) having a disproportionate influence on the results. The summations over year include only those years for which age-composition data are available. The contribution of ρ y
f ,athe age-composition of the discards follows Equations (A.13) and (A.14), except that is
replaced by the model-estimate of the proportion which fish of age a made up of the discards f ,obs ρ y ,aduring year y by sub-fishery f, and is replaced by the observed proportion which fish of age a made up of the discards during year y by sub-fishery f.
The contribution of the catch rate data to the negative of the logarithm of the likelihood function is based on the assumption that fluctuations in catchability are log-normally distributed with a CV of σ q :
f f f 2L = 2 (lnI − ln(q B )) 4 2σ 1
q ∑∑ y y (A.15)
f y
where q f is the catchability coefficient for sub-fishery f, and
I yf is the catch-rate index for sub-fishery f and year y, and
Byf is the mid-season (available) biomass for sub-fishery f and year y:
f f s −Zy a , / 2 B = w (1 − Py a ) S N , es
(A.16) y ∑∑ y a , , a y a s a
The summation over year includes only those years for which catch rate data are available.
The contribution of the egg-production or acoustic estimates to the negative of the logarithm of the likelihood function is given by:
~ obs 2 2L5 = ∑ (By − By ) /(2σ y ) (A.17) y=1994 /5
where Byobs is the estimate of female spawner biomass for year y based on egg-production
or acoustic methods, and
σ y is the standard error of Byobs .
41 APPENDIX